One specific toy is in the shape of a cone mounted on a cylinder. The total height of the toy is 110 mm and the height of its conical part is 77 mm. The diameters of the base of the conical part is 72 mm and that of the cylindrical part is 40 mm.
(iv) If the cost of painting the toy is 2 paise for 8pi mm2 , then what is the cost of painting of a box of 100 toys?
(a) 1598 Rs (b) 2558 Rs (c) 1419 Rs (d) 1894 Rs
Answers
Given :-
- Total height of the toy = 110mm .
- Height of conical part = 77mm.
- Diameter of base of conical part = 72mm.
- Diameter of cylindrical part = 40mm.
- Cost of painting the toy = 2 paise for 8π mm²
To Find :-
- The cost of painting of a box of 100 toys .
Solution :-
we know that,
- Radius = Diameter / 2 .
- CSA of cone = π * radius * slant height.
- Slant height = √[length² + radius²]
- CSA of cylinder = 2 * π * radius * height .
so,
→ Height of conical part = 77mm.
→ Radius of conical part = (72/2) = 36mm.
then,
→ Slant height of conical part = √(77² + 36²) = √(5929 + 1296) = 85 mm.
so,
→ CSA of conical part = π * 36 * 85 = 3060π mm².
also,
→ Base Area of conical part = Base Area of conical part - Base Area of Top of cylinder = π(36)² - π(20)² = π(36² - 20²) = π(36 + 20)(36 - 20) = π * 56 * 16 = 896π mm².
then,
→ Total area to be painted of conical part = 3060π + 896π = 3956π mm².
also,
→ Cylindrical area painted = 2 * π * 20 * 33 + π * (20)² = 1320 π + 400π = 1720 mm².
therefore,
→ Total painted area = 3956π + 1720π = 5676π mm² .
hence,
→ 8π mm² costs = 2 paise
→ π mm² costs = (2/8π) paise
→ 5676π mm² costs = (2/8π) * 5676π = 1419 paise.
∴
→ Cost of painting of a box of 100 toys = 1419 * 100 = 141900 paise = (141900/100) = Rs.1419 (Ans.) (Option C)
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Answer:
Total height of the toy = 110mm .
Height of conical part = 77mm.
Diameter of base of conical part = 72mm.
Diameter of cylindrical part = 40mm.
Cost of painting the toy = 2 paise for 8π mm²
To Find :-
The cost of painting of a box of 100 toys .
Solution :-
we know that,
Radius = Diameter / 2 .
CSA of cone = π * radius * slant height.
Slant height = √[length² + radius²]
CSA of cylinder = 2 * π * radius * height .
so,
→ Height of conical part = 77mm.
→ Radius of conical part = (72/2) = 36mm.
then,
→ Slant height of conical part = √(77² + 36²) = √(5929 + 1296) = 85 mm.
so,
→ CSA of conical part = π * 36 * 85 = 3060π mm².
also,
→ Base Area of conical part = Base Area of conical part - Base Area of Top of cylinder = π(36)² - π(20)² = π(36² - 20²) = π(36 + 20)(36 - 20) = π * 56 * 16 = 896π mm².
then,
→ Total area to be painted of conical part = 3060π + 896π = 3956π mm².
also,
→ Cylindrical area painted = 2 * π * 20 * 33 + π * (20)² = 1320 π + 400π = 1720 mm².
therefore,
→ Total painted area = 3956π + 1720π = 5676π mm² .
hence,
→ 8π mm² costs = 2 paise
→ π mm² costs = (2/8π) paise
→ 5676π mm² costs = (2/8π) * 5676π = 1419 paise.
Step-by-step explanation: